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Theorem anabss5 520
Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss5.1 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
Assertion
Ref Expression
anabss5 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss5
StepHypRef Expression
1 anabss5.1 . . 3 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
21anassrs 386 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
32anabsan 517 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  anabsi5  521  syl2an2r  537  mp3an2ani  1250
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